first of all, you need to put a hash symbol (#) in front of the string denoting the identifier after \quoteDuring.
(Uh. I withdraw. I think it is supposed to be there, but it also works without it. Interesting.)
([OT:] You really should use \relative with some octavation.)

Even then, quoting at the start of a piece is broken. IIRC, it has something to do with the quote being available only after the moment it was declared, but in this very case, it's already needed at the same point in time.
I can't find the bug report right now, so I don't know if there's someone working on this. As a workaround, you can quote the first note for yourself and add the quote later on: